When does a bipartite graph have bounded treewidth?

As the title says, I want to know when the treewidth of a bipartite graph is bounded by a constant. What families of graphs are both bipartite and bounded treewidth?

More generally, I would like to find a property $$P$$ such that for any bipartite graph $$G$$ the following statement is true: "the treewidth of $$G$$ is bound by a constant if and only if $$G$$ satisfies property $$P$$."

I think there is no simpler characterization than just the fact that the treewidth of $$G$$ is bounded. The intuition for why is that by subdividing each edge of a graph we get a bipartite graph with the same treewidth. In particular, we have a very simple reduction from determining the treewidth of a graph to determining the treewidth of a bipartite graph.